Three-Dimensional Lattice Structures for Implants

ABSTRACT

The three-dimensional lattice structures disclosed herein have applications including use in medical implants. Some examples of the lattice structure are structural in that they can be used to provide structural support or mechanical spacing. In some examples, the lattice can be configured as a scaffold to support bone or tissue growth. Some examples can use a repeating modified rhombic dodecahedron or radial dodeca-rhombus unit cell.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/480,383 filed Apr. 1, 2017, U.S. Provisional PatentApplication No. 62/480,393 filed Apr. 1, 2017, and U.S. ProvisionalPatent Application No. 62/619,260 filed Jan. 19, 2018, which are herebyincorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to structures used in medical implantsand, in particular, to structures characterized as a three-dimensionallattice or scaffold.

BACKGROUND OF THE INVENTION

Medical implants can be constructed using a wide range of materials,including metallic materials, Polyether ether ketone (hereinafter“PEEK”), ceramic materials and various other materials or compositesthereof. There are competing priorities when selecting a material for animplant in order for the implant to pass regulatory testing. Somepriorities when designing an implant could include strength, stiffness,fatigue resistance, radiolucency, and bioactivity. Therefore, whendesigning an implant to meet regulatory standards, oftentimes, somecompromises have to be made to meet all testing requirements.

BRIEF SUMMARY OF THE INVENTION

In some embodiments, the present invention provides a lattice structurethat can be useful in applications including medical implants. Thepresent invention can also provide a lattice structure with anisotropicproperties that can be used in medical implants and a method of use. Insome embodiments, the lattice structures disclosed herein can be used toprovide structural support or mechanical spacing. In other embodiments,the lattice structures disclosed herein can provide a scaffold for bonegrowth.

The structures described herein may be constructed from a range ofmaterials with or without additional surface treatments or coatings. Thelattice structures can use a repeating geometric pattern in someembodiments, where a unit cell can be repeated over a volume. Some unitcells that are disclosed include a modified rhombic dodecahedron unitcell and a radial dodeca-rhombus unit cell.

While the embodiments expressed herein are directed towards medicalimplants, the structures disclosed could also be beneficial when used inmedical devices outside of the body that require a high strengthcompared to volumetric density. Other medical devices that could includeone or more embodiments described herein include, but are not limitedto, external casts or splints, prostheses, orthoses, ports, guides,markers, superstructures, or exoskeletons.

In particular, cancellous bone has anisotropic properties and possessesdifferent mechanical properties in different directions. For instance,bone in the spine can be more stiff in the rostral-caudal direction sothat a load that would fracture the bone in the anterior to posteriordirection would only cause an elastic deformation in the rostral-caudaldirection. Matching an implant's properties to the surrounding bone atan implant site is important because a mismatch in strength or stiffnesscan have an effect on the strength of new bone growth. According toWolff's Law, bone will adapt to the physiological stresses put on itover time, becoming stronger in response when loaded and becoming weakerwhen not loaded. Therefore, reducing the load that a new bone formationexperiences can reduce the mechanical strength of the new boneformation.

In some embodiments, the present invention provides biocompatiblestructures with anisotropic properties and a method of use. Inparticular, some embodiments of the present invention can becharacterized as having an elastic modulus in one direction and at leasta second elastic modulus in another direction. Directions, as usedherein, are used in reference to the three-dimensional Cartesiancoordinates where the x axis and y axis are horizontal and the z axis isvertical (also described herein as the x, y and z “direction”). Theelastic modulus, when used to describe a lattice, implant or structureof any kind, refers to both or either of the design elastic modulus orthe actual elastic modulus. The design elastic modulus of a lattice,implant or structure is the elastic modulus calculated based on itsstructural configuration and its material composition. The actualelastic modulus refers to the elastic modulus of a lattice, implant orstructure after it has been manufactured. The actual elastic modulus canvary from the design elastic modulus due to changes or variations withinmanufacturing tolerances. For example, a lattice, implant or structurethat is overbuilt within an acceptable tolerance during manufacturingcould have a higher actual elastic modulus than the design elasticmodulus. In many situations, the actual elastic modulus can becalculated using a correction factor, creating an approximate actualelastic modulus. An approximate actual elastic modulus generallyquantifies the expected actual elastic modulus of a lattice, implant orstructure when testing of a manufactured article has not been completed.Since a lattice, implant or structure of any kind can be easily designedusing a design elastic modulus or to an approximate actual elasticmodulus through the application of a correction factor, the use of theterm “elastic modulus” herein can refer to both or either designparameter.

Some embodiments disclosed herein can be useful as a scaffold for bonegrowth. In some examples, the scaffolds can be structural, meaning thatthey provide structural support or mechanical spacing, and in otherexamples, the scaffolds can be nonstructural. In examples that use astructural scaffold, the material can provide support that more closelymimics the properties of naturally occurring bone. For instance,cancellous bone has anisotropic properties and it could be appropriateto use a lattice structure with anisotropic properties, as disclosedherein, as a bone growth scaffold in areas including the spine. Thepresent invention can also be used in other applications where ascaffold for bone growth with different mechanical properties in atleast two directions is desirable. In another example, it may bedesirable for a scaffold to load bone in one or more directions ofreduced stiffness and not in one or more directions of shielding orincreased stiffness to promote preferential bone growth in thedirection(s) of loading.

Many of the exemplary embodiments presented in this application areoptimized for use as a scaffold for bone in spine, however, it isappreciated that the invention could be used with other types bone andother types of tissue within the inventive concept expressed herein.

In one exemplary embodiment of an anisotropic lattice structure is anelongated modified rhombic dodecahedron lattice that has been elongatedin the x and y axes relative to the z axis. The elongated modifiedrhombic dodecahedron lattice is presented as a single cell defined bystruts, with additional struts extending away from the cell to showportions of the repeating structure. The unit cell may be repeated in alattice structure to achieve an open cell structure of the desiredvolume and mechanical properties.

In a second exemplary embodiment of an anisotropic lattice is a groupingof three elongated modified rhombic dodecahedron cells that have beenelongated in the x and y axes relative to the z axis. The grouping ispresented as three unit cells defined by struts, in a stackedarrangement, with additional struts extending away from the cell to showportions of the repeating structure.

The disclosed embodiments of the present invention can be used in amethod of reducing stress shielding. It can be especially beneficial toreduce stress shielding in spinal fusion procedures. The anisotropicunit cells of the present invention can be repeated to form ananisotropic lattice or scaffold for use in spinal fusion procedures. Theanisotropic lattice can provide mechanical spacing between the endplatesof the adjacent vertebrae and provide a scaffold for bone growth. Theanisotropic properties of the present invention can allow a reducedelastic modulus in the superior to inferior direction, allowing new bonegrowth to be subject to physiological forces of the load-bearing spine.The reduction in stress shielding can result in stronger new bonegrowth.

The anisotropic properties may allow reduced stiffness in one or moredirections of bone growth while possessing the requisite stiffness inone or more directions of off-axis biomechanical loading and loadingrequired for device testing. When elongating a unit cell in a direction,the elongation can change the strut angle and decrease the stiffness ofthe unit cell in a direction normal to the elongation.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. A1 is an isometric view of a single modified rhombic dodecahedronunit cell containing a full modified rhombic dodecahedron structurealong with radial struts that comprise portions of adjacent unit cells.

FIG. A2 is a side view of a single modified rhombic dodecahedron unitcell showing the configuration of interconnections when viewed from alateral direction.

FIG. A3 is a side view of a single modified rhombic dodecahedron unitcell where the central void is being measured using the longestdimension method.

FIG. A4 is a side view of a single modified rhombic dodecahedron unitcell where an interconnection is being measured using the longestdimension method.

FIG. A5 is a side view of the central void of a modified rhombicdodecahedron unit cell being measured with the largest sphere method.

FIG. A6 is a view from a direction normal to the planar direction of aninterconnection being measured with the largest sphere method.

FIG. A7 is an isometric view of a single radial dodeca-rhombus unitcell.

FIG. A8 is a side view of a single radial dodeca-rhombus unit cell.

FIG. A9 is an isometric view of an example of a single node and singlestrut combination that could be used in a radial dodeca-rhombus unitcell.

FIG. A10 is a side view of an example of a single node and single strutcombination that could be used in a radial dodeca-rhombus unit cell.

FIG. A11 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately3 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. A12 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately4 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. A13 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately10 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. A14 is a side view of a single node and two adjacent struts viewedfrom the corner of the volume defining the bounds of the combination andthe lateral separation angle.

FIG. A15 is an isometric view of a sub-unit cell comprised of a singlenode and four struts.

FIG. A16 is an isometric view of two sub-unit cells in a stackedformation where the upper sub-unit cell is inverted and fixed to the topof the lower sub-unit cell.

FIG. A17 is an isometric view of eight sub-unit cells stacked togetherto form a single unit cell.

FIG. 1 is an isometric view of a modified rhombic dodecahedron lattice.

FIG. 2 is a front view of a modified rhombic dodecahedron lattice.

FIG. 3 is a bottom view of a modified rhombic dodecahedron lattice.

FIG. 4 is an isometric view of a first exemplary embodiment of ananisotropic lattice structure, showing an elongated modified rhombicdodecahedron lattice.

FIG. 5 is a front view of a first exemplary embodiment of an anisotropiclattice structure, showing an elongated modified rhombic dodecahedronlattice.

FIG. 6 is a is a bottom view of a first exemplary embodiment of ananisotropic lattice structure, showing an elongated modified rhombicdodecahedron lattice.

FIG. 7 is an isometric view of a second exemplary embodiment of ananisotropic lattice structure, showing an alternate elongated modifiedrhombic dodecahedron lattice.

FIG. 8 is a front view of a second exemplary embodiment of ananisotropic lattice structure, showing an alternate elongated modifiedrhombic dodecahedron lattice.

FIG. 9 is a bottom view of a second exemplary embodiment of ananisotropic lattice structure, showing an alternate elongated modifiedrhombic dodecahedron lattice.

DETAILED DESCRIPTION OF THE INVENTION

In many situations, it is desirable to use an implant that is capable ofbone attachment or osteointegration over time. It is also desirable inmany situations to use an implant that is capable of attachment orintegration with living tissue. Examples of implants where attachment tobone or osteointegration is beneficial include, but are not limited to,cervical, lumbar, and thoracic interbody fusion implants, vertebral bodyreplacements, osteotomy wedges, dental implants, bone stems, acetabularcups, cranio-facial plating, bone replacement and fracture plating. Inmany applications, it is also desirable to stress new bone growth toincrease its strength. According to Wolff's law, bone will adapt tostresses placed on it so that bone under stress will grow stronger andbone that isn't stressed will become weaker.

In some aspects, the systems and methods described herein can bedirected toward implants that are configured for osteointegration andstimulating adequately stressed new bone growth. Many of the exemplaryimplants of the present invention are particularly useful for use insituations where it is desirable to have strong bone attachment and/orbone growth throughout the body of an implant. Whether bone growth isdesired only for attachment or throughout an implant, the presentinvention incorporates a unique lattice structure that can providemechanical spacing, a scaffold to support new bone growth and a modulusof elasticity that allows new bone growth to be loaded withphysiological forces. As a result, the present invention providesimplants that grow stronger and healthier bone for more secureattachment and/or for a stronger bone after the implant osteointegrates.

The exemplary embodiments of the invention presented can be comprised,in whole or in part, of a lattice. A lattice, as used herein, refers toa three-dimensional material with one or more interconnected openingsthat allow a fluid to communicate from one location to another locationthrough an opening. A three-dimensional material refers to a materialthat fills a three-dimensional space (i.e. has height, width andlength). Lattices can be constructed by many means, including repeatingvarious geometric shapes or repeating random shapes to accomplish amaterial with interconnected openings. An opening in a lattice is anyarea within the bounds of the three-dimensional material that is devoidof that material. Therefore, within the three-dimensional boundaries ofa lattice, there is a volume of material and a volume that is devoid ofthat material.

The material that provides the structure of the lattice is referred toas the primary material. The structure of a lattice does not need toprovide structural support for any purpose, but rather refers to theconfiguration of the openings and interconnections that comprise thelattice. An opening in a lattice may be empty, filled with a gaseousfluid, filled with a liquid fluid, filled with a solid or partiallyfilled with a fluid and/or solid. Interconnections, with respect toopenings, refer to areas devoid of the primary material and that link atleast two locations together. Interconnections may be configured toallow a fluid to pass from one location to another location.

A lattice can be defined by its volumetric density, meaning the ratiobetween the volume of the primary material and the volume of voidspresented as a percentage for a given three-dimensional material. Thevolume of voids is the difference between the volume of the bounds ofthe three-dimensional material and the volume of the primary material.The volume of voids can comprise of the volume of the openings, thevolume of the interconnections and/or the volume of another materialpresent. For example, a lattice with a 30% volumetric density would becomprised of 30% primary material by volume and 70% voids by volume overa certain volume. A lattice with a 90% volumetric density would becomprised of 90% primary material by volume and 10% voids by volume overa certain volume. In three-dimensional materials with a volumetricdensity of less than 50%, the volume of the primary material is lessthan the volume of voids. While the volumetric density refers to thevolume of voids, the voids do not need to remain void and can be filled,in whole or in part, with a fluid or solid prior to, during or afterimplantation.

Lattices comprised of repeating geometric patterns can be describedusing the characteristics of a repeating unit cell. A unit cell in arepeating geometric lattice is a three-dimensional shape capable ofbeing repeated to form a lattice. A repeating unit cell can refer tomultiple identical unit cells that are repeated over a lattice structureor a pattern through all or a portion of a lattice structure. Each unitcell is comprised of a certain volume of primary material and a certainvoid volume, or in other words, a spot volumetric density. The spotvolumetric density may cover as few as a partial unit cell or aplurality of unit cells. In many situations, the spot volumetric densitywill be consistent with the material's volumetric density, but there aresituations where it could be desirable to locally increase or decreasethe spot volumetric density.

Unit cells can be constructed in numerous volumetric shapes containingvarious types of structures. Unit cells can be bound by a defined volumeof space to constrict the size of the lattice structure or other type ofstructure within the unit cell. In some embodiments, unit cells can bebound by volumetric shapes, including but not limited to, a cubicvolume, a cuboid volume, a hexahedron volume or an amorphous volume. Theunit cell volume of space can be defined based on a number of faces thatmeet at corners. In examples where the unit cell volume is a cubic,cuboid or hexahedron volume, the unit cell volume can have six faces andeight corners, where the corners are defined by the location where threefaces meet. Unit cells may be interconnected in some or all areas, notinterconnected in some or all areas, of a uniform size in some or allareas or of a nonuniform size in some or all areas. In some embodimentsdisclosed herein that use a repeating geometric pattern, the unit cellscan be defined by a number of struts defining the edges of the unit celland joined at nodes about the unit cell. Unit cells so defined can sharecertain struts among more than one unit cell, so that two adjacent unitcells may share a common planar wall defined by struts common to bothcells. In some embodiments disclosed herein that use a repeatinggeometric pattern, the unit cells can be defined by a node and a numberof struts extending radially from that node.

While the present application uses volumetric density to describeexemplary embodiments, it is also possible to describe them using othermetrics, including but not limited to cell size, strut size orstiffness. Cell size may be defined using multiple methods, includingbut not limited to cell diameter, cell width, cell height and cellvolume. Strut size may be defined using multiple methods, including butnot limited to strut length and strut diameter.

Repeating geometric patterns are beneficial for use in latticestructures contained in implants because they can provide predictablecharacteristics. Many repeating geometric shapes may be used as the unitcell of a lattice, including but are not limited to, rhombicdodecahedron, diamond, dodecahedron, square, pentagonal, hexagonal,octagonal, sctet struts, trunic octa, diagonal struts, other knowngeometric structures, and rounded, reinforced, weakened, or simplifiedversions of each geometry.

Lattices may also be included in implants as a structural component or anonstructural component. Lattices used in structural applications may bereferred to herein as structural lattices, load-bearing lattices orstressed lattices. In some instances, structural lattices, load-bearinglattices or stressed lattices may be simply referred to as a lattice.Repeating geometric shaped unit cells, particularly the rhombicdodecahedron, are well suited, in theory, for use in structural latticesbecause of their strength to weight ratio. To increase the actualstrength and fatigue resistance of a rhombic dodecahedron lattice, thepresent invention, in some embodiments, includes a modified strutcomprised of triangular segments, rather than using a strut with arectangular or circular cross section. Some embodiments herein alsomodify the angles defining the rhombic faces of a rhombic dodecahedronto change the lattice's elastic modulus and fatigue resistance. The useof triangular segments provides a lattice with highly predictableprinted properties that approach the theoretical strength values for arhombic dodecahedron lattice.

In structural lattice applications, the strength and elastic modulus ofthe lattice can be approximated by the volumetric density. When thevolumetric density increases, the strength and the elastic modulusincreases. Compared to other porous structures, the lattice of thepresent invention has a higher strength and elastic modulus for a givenvolumetric density because of its ability to use the high strength toweight benefits of a rhombic dodecahedron, modified rhombic dodecahedronor radial dodeca-rhombus unit cell.

When configured to provide support for bone or tissue growth, a latticemay be referred to as a scaffold. Lattices can be configured to supportbone or tissue growth by controlling the size of the openings andinterconnections disposed within the three-dimensional material. Ascaffold, if used on the surface of an implant, may provide anosteointegration surface that allows adjacent bone to attach to theimplant. A scaffold may also be configured to provide a path that allowsbone to grow further than a mere surface attachment. Scaffolds intendedfor surface attachment are referred to herein as surface scaffolds. Asurface scaffold may be one or more unit cells deep, but does not extendthroughout the volume of an implant. Scaffolds intended to supportin-growth beyond mere surface attachment are referred to herein as bulkscaffolds. Scaffolds may also be included in implants as a structuralcomponent or a nonstructural component. Scaffolds used in structuralapplications may be referred to herein as structural scaffolds,load-bearing scaffolds or stressed scaffolds. In some instances,structural scaffolds, load-bearing scaffolds or stressed scaffolds maybe simply referred to as a scaffold. In some instances, the use of theterm scaffold may refer to a material configured to provide support forbone or tissue growth, where the material is not a lattice.

The scaffolds described herein can be used to promote the attachment orin-growth of various types of tissue found in living beings. As notedearlier, some embodiments of the scaffold are configured to promote boneattachment and in-growth. The scaffolds can also be configured topromote attachment of in-growth of other areas of tissue, such asfibrous tissue. In some embodiments, the scaffold can be configured topromote the attachment or in-growth of multiple types of tissue. Someembodiments of the scaffolds are configured to be implanted near orabutting living tissue. Near living tissue includes situations whereother layers, materials or coatings are located between a scaffold andany living tissue.

In some embodiments, the present invention uses bulk scaffolds withopenings and interconnections that are larger than those known in theart. Osteons can range in diameter from about 100 μm and it is theorizedthat a bundle of osteons would provide the strongest form of new bonegrowth. Bone is considered fully solid when it has a diameter of greaterthan 3 mm so it is theorized that a bundle of osteons with a diameterequaling approximately half of that value would provide significantstrength when grown within a scaffold. It is also theorized that osteonsmay grow in irregular shapes so that the cross-sectional area of anosteon could predict its strength. A cylindrical osteon growth with a 3mm diameter has a cross-sectional area of approximately 7 square mm anda cylindrical osteon with a 1.5 mm diameter has a cross-sectional areaof 1.8 square mm. It is theorized that an osteon of an irregular shapewith a cross-sectional area of at least 1.8 square millimeters couldprovide a significant strength advantage when grown in a scaffold.

Most skilled in the art would indicate that pores or openings with adiameter or width between 300 μm to 900 μm, with a pore side of 600 μmbeing ideal, provide the best scaffold for bone growth. Instead, someembodiments of the present invention include openings andinterconnections with a diameter or width on the order of 1.0 to 15.0times the known range, with the known range being 300 μm to 900 μm,resulting in openings from 0.07 mm² up to 145 mm² cross sectional areafor bone growth. In some examples, pores or openings with a diameter orwidth between and including 100 μm to 300 μm could be beneficial. Someexamples include openings and interconnections with a diameter on theorder of 1.0 to 5.0 times the known range. It has been at leasttheorized that the use of much larger openings and interconnections thanthose known in the art will allow full osteons and solid bone tissue toform throughout the bulk scaffold, allowing the vascularization of new,loadable bone growth. In some examples, these pores may be 3 mm indiameter or approximately 7 mm² in cross sectional area. In otherexamples, the pores are approximately 1.5 mm in diameter orapproximately 1.75 mm² in cross sectional area. The use of only thesmaller diameter openings and interconnections known in the art aretheorized to limit the penetration of new bone growth into a bulkscaffold because the smaller diameter openings restrict the ability ofvascularization throughout the bulk scaffold.

A related structure to a lattice is a closed cell material. A closedcell material is similar to a lattice, in that it has openings containedwithin the bounds of a three-dimensional material, however, closed cellmaterials generally lack interconnections between locations throughopenings or other pores. A closed cell structure may be accomplishedusing multiple methods, including the filling of certain cells orthrough the use of solid walls between the struts of unit cells. Aclosed cell structure can also be referred to as a cellular structure.It is possible to have a material that is a lattice in one portion and aclosed cell material in another. It is also possible to have a closedcell material that is a lattice with respect to only certaininterconnections between openings or vice versa. While the focus of thepresent disclosure is on lattices, the structures and methods disclosedherein can be easily adapted for use on closed cell structures withinthe inventive concept.

The lattice used in the present invention can be produced from a rangeof materials and processes. When used as a scaffold for bone growth, itis desirable for the lattice to be made of a biocompatible material thatallows for bone attachment, either to the material directly or throughthe application of a bioactive surface treatment. In one example, thescaffold is comprised of an implantable metal. Implantable metalsinclude, but are not limited to, zirconium, stainless steel (316 &316L), tantalum, nitinol, cobalt chromium alloys, titanium and tungsten,and alloys thereof. Scaffolds comprised of an implantable metal may beproduced using an additive metal fabrication or 3D printing process.Appropriate production processes include, but are not limited to, directmetal laser sintering, selective laser sintering, selective lasermelting, electron beam melting, laminated object manufacturing anddirected energy deposition.

In another example, the lattice of the present invention is comprised ofan implantable metal with a bioactive coating. Bioactive coatingsinclude, but are not limited to, coatings to accelerate bone growth,anti-thrombogenic coatings, anti-microbial coatings, hydrophobic orhydrophilic coatings, and hemophobic, superhemophobic, or hemophiliccoatings. Coatings that accelerate bone growth include, but are notlimited to, calcium phosphate, hydroxyapatite (“HA”), silicate glass,stem cell derivatives, bone morphogenic proteins, titanium plasma spray,titanium beads and titanium mesh. Anti-thrombogenic coatings include,but are not limited to, low molecular weight fluoro-oligomers.Anti-microbial coatings include, but are not limited to, silver,organosilane compounds, iodine and silicon-nitride. Superhemophobiccoatings include fluorinated nanotubes.

In another example, the lattice is made from a titanium alloy with anoptional bioactive coating. In particular, Ti6Al4V ELI wrought (AmericanSociety for Testing and Materials (“ASTM”) F136) is a particularlywell-suited titanium alloy for scaffolds. While Ti6Al4V ELI wrought isthe industry standard titanium alloy used for medical purposes, othertitanium alloys, including but not limited to, unalloyed titanium (ASTMF67), Ti6Al4V standard grade (ASTM F1472), Ti6Al7Nb wrought (ASTM 1295),Ti5Al2.5Fe wrought (British Standards Association/International StandardOrganization Part 10), CP and Ti6Al4V standard grade powders (ASTMF1580), Ti13Nb13Zr wrought (ASTM F1713), the lower modulusTi-24Nb-4Zr-8Sn and Ti12Mo6Zr2Fe wrought (ASTM F1813) can be appropriatefor various embodiments of the present invention.

Titanium alloys are an appropriate material for scaffolds because theyare biocompatible and allow for bone attachment. Various surfacetreatments can be done to titanium alloys to increase or decrease thelevel of bone attachment. Bone will attach to even polished titanium,but titanium with a surface texture allows for greater bone attachment.Methods of increasing bone attachment to titanium may be producedthrough a forging or milling process, sandblasting, acid etching, andthe use of a bioactive coating. Titanium parts produced with an additivemetal fabrication or 3D printing process, such as direct metal lasersintering, can be treated with an acid bath to reduce surface stressrisers, normalize surface topography, and improve surface oxide layer,while maintaining surface roughness and porosity to promote boneattachment.

Additionally, Titanium or other alloys may be treated with heparin,heparin sulfate (HS), glycosaminoglycans (GAG), chondroitin-4-sulphate(C4S), chondroitin-6-sulphate (C6S), hyaluronan (HY), and otherproteoglycans with or without an aqueous calcium solution. Suchtreatment may occur while the material is in its pre-manufacturing form(often powder) or subsequent to manufacture of the structure.

While a range of structures, materials, surface treatments and coatingshave been described, it is believed that a lattice using a repeatingmodified rhombic dodecahedron (hereinafter “MRDD”) unit cell can presenta preferable combination of stiffness, strength, fatigue resistance, andconditions for bone ingrowth. In some embodiments, the repeating MRDDlattice is comprised of titanium or a titanium alloy. A generic rhombicdodecahedron (hereinafter “RDD”), by definition, has twelve sides in theshape of rhombuses. When repeated in a lattice, an RDD unit cell iscomprised of 24 struts that meet at 14 vertices. The 24 struts definethe 12 planar faces of the structure and disposed at the center of eachplanar face is an opening, or interconnection, allowing communicationfrom inside the unit cell to outside the unit cell.

An example of the MRDD unit cell B10 used in the present invention isshown in FIGS. A1-A5. In FIG. A1 is an isometric view of a single MRDDunit cell B10 containing a full MRDD structure along with radial strutsthat comprise portions of adjacent unit cells. In FIG. A2 is a side viewof a single MRDD unit cell B10 showing the configuration ofinterconnections when viewed from a lateral direction. A top or bottomview of the MRDD unit cell B10 would be substantially the same as theside view depicted in FIG. A2. The MRDD unit cell B10 differs in bothstructural characteristics and method of design from generic RDD shapes.A generic RDD is comprised of 12 faces where each face is an identicalrhombus with an acute angle of 70.5 degrees and an obtuse angle of 109.5degrees. The shape of the rhombus faces in a generic RDD do not changeif the size of the unit cell or the diameter of the struts are changedbecause the struts are indexed based on their axis and each pass throughthe center of the 14 nodes or vertices.

In some embodiments of the MRDD, each node is contained within a fixedvolume that defines its bounds and provides a fixed point in space forthe distal ends of the struts. The fixed volume containing the MRDD or asub-unit cell of the MRDD can be various shapes, including but notlimited to, a cubic, cuboid, hexahedron or amorphous volume. Someexamples use a fixed volume with six faces and eight corners defined bylocations where three faces meet. The orientation of the struts can bebased on the center of a node face at its proximate end and the nearestcorner of the volume to that node face on its distal end. Each node ispreferably an octahedron, more specifically a square bipyramid (i.e. apyramid and inverted pyramid joined on a horizontal plane). Each node,when centrally located in a cuboid volume, more preferably comprises asquare plane parallel to a face of the cuboid volume, six vertices andis oriented so that each of the six vertices are positioned at theirclosest possible location to each of the six faces of the cuboid volume.Centrally located, with regards to the node's location within a volumerefers to positioning the node at a location substantially equidistantfrom opposing walls of the volume. In some embodiments, the node canhave a volumetric density of 100 percent and in other embodiments, thenode can have a volumetric density of less than 100 percent. Each faceof the square bipyramid node can be triangular and each face can providea connection point for a strut.

The struts can also be octahedrons, comprising an elongate portion ofsix substantially similar elongate faces and two end faces. The elongatefaces can be isosceles triangles with a first internal angle, angle A,and a second internal angle, angle B, where angle B is greater thanangle A. The end faces can be substantially similar isosceles trianglesto one another with a first internal angle, angle C, and a secondinternal angle, angle D, where angle D is greater than angle C.Preferably, angle C is greater than angle A.

The strut direction of each strut is a line or vector defining theorientation of a strut and it can be orthogonal or non-orthogonalrelative to the planar surface of each node face. In the MRDD and radialdodeca-rhombus structures disclosed herein, the strut direction can bedetermined using a line extending between the center of the strut endfaces, the center of mass along the strut or an external edge or face ofthe elongate portion of the strut. When defining a strut direction usinga line extending between the center of the strut end faces, the line isgenerally parallel to the bottom face or edge of the strut. Whendefining a strut direction using a line extending along the center ofmass of the strut, the line can be nonparallel to the bottom face oredge of the strut. The octahedron nodes of the MRDD can be scaled toincrease or decrease volumetric density by changing the origin point andsize of the struts. The distal ends of the struts, however, are lockedat the fixed volume corners formed about each node so that their anglerelative to each node face changes as the volumetric density changes.Even as the volumetric density of an MRDD unit cell changes, thedimensions of the fixed volume formed about each node does not change.In FIG. A1, dashed lines are drawn between the corners of the MRDD unitcell B10 to show the cube B11 that defines its bounds. In the MRDD unitcell in FIG. A1, the height B12, width B13 and depth B14 of the unitcell are substantially the same, making the area defined by B11 a cube.

In some embodiments, the strut direction of a strut can intersect thecenter of the node and the corner of the cuboid volume nearest to thenode face where the strut is fixed. In some embodiments, the strutdirection of a strut can intersect just the corner of the cuboid volumenearest to the node face where the strut is fixed. In some embodiments,a reference plane defined by a cuboid or hexahedron face is used todescribe the strut direction of a strut. When the strut direction of astrut is defined based on a reference plane, it can be between 0 degreesand 90 degrees from the reference plane. When the strut direction of astrut is defined based on a reference plane, it is preferably eightdegrees to 30 degrees from the reference plane.

By indexing the strut orientation to a variable node face on one end anda fixed point on its distal end, the resulting MRDD unit cell can allowrhombus shaped faces with a smaller acute angle and larger obtuse anglethan a generic RDD. The rhombus shaped faces of the MRDD can have twosubstantially similar opposing acute angles and two substantiallysimilar opposing obtuse angles. In some embodiments, the acute anglesare less than 70.5 degrees and the obtuse angles are greater than 109.5degrees. In some embodiments, the acute angles are between 0 degrees and55 degrees and the obtuse angles are between 125 degrees and 180degrees. In some embodiments, the acute angles are between 8 degrees and60 degrees and the obtuse angles are between 120 degrees and 172degrees. The reduction in the acute angles increases fatigue resistancefor loads oriented across the obtuse angle corner to far obtuse anglecorner. The reduction in the acute angles and increase in obtuse anglesalso orients the struts to increase the MRDD's strength in shear andincreases the fatigue resistance. By changing the rhombus corner anglesfrom a generic RDD, shear loads pass substantially in the axialdirection of some struts, increasing the shear strength. Changing therhombus corner angles from a generic RDD also reduces overall deflectioncaused by compressive loads, increasing the fatigue strength byresisting deflection under load.

When placed towards the center of a lattice structure, the 12interconnections of a unit cell connect to 12 different adjacent unitcells, providing continuous paths through the lattice. The size of thecentral void and interconnections in the MRDD may be defined using thelongest dimension method as described herein. Using the longestdimension method, the central void can be defined by taking ameasurement of the longest dimension as demonstrated in FIG. A3. In FIG.A3, the longest dimension is labeled as distance AA. The distance AA canbe taken in the vertical or horizontal directions (where the directionsreference the directions on the page) and would be substantially thesame in this example. The interconnections may be defined by theirlongest measurement when viewed from a side, top or bottom of a unitcell. In FIG. A4, the longest dimension is labeled as distance AB. Thedistance AB can be taken in the vertical or horizontal directions (wherethe directions reference the directions on the page). The view in FIG.A4 is a lateral view, however, in this example the unit cell will appearsubstantially the same when viewed from the top or bottom.

The size of the central void and interconnections can alternatively bedefined by the largest sphere method as described herein. Using thelargest sphere method, the central void can be defined by the diameterof the largest sphere that can fit within the central void withoutintersecting the struts. In FIG. A5 is an example of the largest spheremethod being used to define the size of a central void with a spherewith a diameter of BA. The interconnections are generally rhombus shapedand their size can alternatively be defined by the size of the lengthand width of three circles drawn within the opening. Drawn within theplane defining a side, a first circle BB1 is drawn at the center of theopening so that it is the largest diameter circle that can fit withoutintersecting the struts. A second circle BB2 and third circle BB3 isthem drawn so that they are tangential to the first circle BB1 and thelargest diameter circles that can fit without intersecting the struts.The diameter of the first circle BB1 is the width of the interconnectionand the sum of the diameters of all three circles BB1, BB2 & BB3represents the length of the interconnection. Using this method ofmeasurement removes the acute corners of the rhombus shaped opening fromthe size determination. In some instances, it is beneficial to removethe acute corners of the rhombus shaped opening from the calculated sizeof the interconnections because of the limitations of additivemanufacturing processes. For example, if an SLS machine has a resolutionof 12 μm where the accuracy is within 5 μm, it is possible that theacute corner could be rounded by the SLS machine, making it unavailablefor bone ingrowth. When designing lattices for manufacture on lessprecise additive process equipment, it can be helpful to use thismeasuring system to better approximate the size of the interconnections.

Using the alternative measuring method, in some examples, the width ofthe interconnections is approximately 600 μm and the length of theinterconnections is approximately 300 μm. The use of a 600 μm length and300 μm width provides an opening within the known pore sizes for bonegrowth and provides a surface area of roughly 1.8 square millimeters,allowing high strength bone growth to form. Alternative embodiments maycontain interconnections with a cross sectional area of 1.0 to 15.0times the cross-sectional area of a pore with a diameter of 300 μm.Other embodiments may contain interconnections with a cross sectionalarea of 1.0 to 15.0 times the cross-sectional area of a pore with adiameter of 900 μm.

The MRDD unit cell also has the advantage of providing at least two setsof substantially homogenous pore or opening sizes in a latticestructure. In some embodiments, a first set of pores have a width ofabout 200 μm to 900 μm and a second set of pores have a width of about 1to 15 times the width of the first set of pores. In some embodiments, afirst set of pores can be configured to promote the growth ofosteoblasts and a second set of pores can be configured to promote thegrowth of osteons.

Pores sized to promote osteoblast growth can have a width of between andincluding about 100 μm to 900 μm. In some embodiments, pores sized topromote osteoblast growth can have a width that exceeds 900 μm. Poressized to promote the growth of osteons can have a width of between andincluding about 100 μm to 13.5 mm. In some embodiments, pores sized topromote osteon growth can have a width that exceeds 13.5 mm.

In some embodiments, it is beneficial to include a number ofsubstantially homogenous larger pores and a number of substantiallyhomogenous smaller pores, where the number of larger pores is selectedbased on a ratio relative to the number of smaller pores. For example,some embodiments have one large pore for every one to 25 small pores inthe lattice structure. Some embodiments preferably have one large porefor every eight to 12 smaller pores. In some embodiments, the number oflarger and smaller pores can be selected based on a percentage of thetotal number of pores in a lattice structure. For example, someembodiments can include larger pores for four percent to 50 percent ofthe total number of pores and smaller pores for 50 percent to 96 percentof the total number of pores. More preferably, some embodiments caninclude larger pores for about eight percent to 13 percent of the totalnumber of pores and smaller pores for about 87 percent to 92 percent ofthe total number of pores. It is believed that a lattice constructedwith sets of substantially homogenous pores of the disclosed two sizesprovides a lattice structure that simultaneously promotes osteoblast andosteon growth.

The MRDD unit cell may also be defined by the size of theinterconnections when viewed from a side, top or bottom of a unit cell.The MRDD unit cell has the same appearance when viewed from a side, topor bottom, making the measurement in a side view representative of theothers. When viewed from the side, as in FIG. A4, an MRDD unit celldisplays four distinct diamond shaped interconnections withsubstantially right angles. The area of each interconnection is smallerwhen viewed in the lateral direction than from a direction normal to theplanar direction of each interconnection, but the area when viewed inthe lateral direction can represent the area available for bone to growin that direction. In some embodiments, it may be desirable to index theproperties of the unit cell and lattice based on the area of theinterconnections when viewed from the top, bottom or lateral directions.

In some embodiments of the lattice structures disclosed herein, thecentral void is larger than the length or width of the interconnections.Because the size of each interconnection can be substantially the samein a repeating MRDD structure, the resulting lattice can be comprised ofopenings of at least two discrete sizes. In some embodiments, it ispreferable for the diameter of the central void to be approximately twotimes the length of the interconnections. In some embodiments, it ispreferable for the diameter of the central void to be approximately fourtimes the width of the interconnections.

In some embodiments, the ratio between the diameter of the central voidand the length or width of the interconnections can be changed to createa structural lattice of a particular strength. In these embodiments,there is a correlation where the ratio between the central void diameterand the length or width of the interconnections increases as thestrength of the structural lattice increases.

It is also believed that a lattice using a repeating radialdodeca-rhombus (hereinafter “RDDR”) unit cell can present a preferablecombination of stiffness, strength, fatigue resistance, and conditionsfor bone ingrowth. In some embodiments, the repeating RDDR lattice iscomprised of titanium or a titanium alloy. In FIG. A7 is an isometricview of a single RDDR unit cell B20 containing a full RDDR structure. InFIG. A8 is a side view of a single RDDR unit cell B20 showing theconfiguration of interconnections when viewed from a lateral direction.A top or bottom view of the RDDR unit cell B20 would be substantiallythe same as the side view depicted in FIG. A8.

As used herein, an RDDR unit cell B20 is a three-dimensional shapecomprised of a central node with radial struts and mirrored strutsthereof forming twelve rhombus shaped structures. The node is preferablyan octahedron, more specifically a square bipyramid (i.e. a pyramid andinverted pyramid joined on a horizontal plane). Each face of the node ispreferably triangular and fixed to each face is a strut comprised of sixtriangular facets and two end faces. The central axis of each strut canbe orthogonal or non-orthogonal relative to the planar surface of eachnode face. The central axis may follow the centroid of the strut. TheRDDR is also characterized by a central node with one strut attached toeach face, resulting in a square bipyramid node with eight strutsattached.

Examples of node and strut combinations are shown in FIGS. A9-A13. InFIG. A9 is an isometric view of a single node B30 with a single strutB31 attached. The node B30 is a square bipyramid oriented so that twopeaks face the top and bottom of a volume B32 defining the bounds of thenode B30 and any attached strut(s) B31. The node B30 is oriented so thatthe horizontal corners are positioned at their closest point to thelateral sides of the volume B32. The strut B31 extends from a node B30face to the corner of the volume B32 defining the bounds of the node andattached struts. In FIG. A9, the central axis of the strut is 45 degreesabove the horizontal plane where the node's planar face is 45 degreesabove a horizontal plane.

FIG. A9 also details an octahedron strut B31, where dashed lines showhidden edges of the strut. The strut B31 is an octahedron with anelongate portion of six substantially similar elongate faces and two endfaces. The elongate faces B31 a, B31 b, B31 c, B31 d, B31 e & B31 f ofthe strut B31 define the outer surface of the strut's elongate andsomewhat cylindrical surface. Each of the elongate faces B31 a, B31 b,B31 c, B31 d, B31 e & B31 f are isosceles triangles with a firstinternal angle, angle A, and a second internal angle, angle B, whereangle B is greater than angle A. The strut B31 also has two end facesB31 f & B31 g that isosceles triangles that are substantially similar toone another, having a first internal angle, angle C, and a secondinternal angle, angle D, and where angle D is greater than angle C. Whencomparing the internal angles of the elongate faces B31 a, B31 b, B31 c,B31 d, B31 e & B31 f to the end faces B31 f& B31 g, angle C is greaterthan angle A.

In FIG. A10 is a side view of the node B30 and strut B31 combinationbounded by volume B32. In the side view, the height of the node B30compared to the height of the cube B32 can be compared easily. In FIGS.A11-A13 are side views of node and strut combinations viewed from acorner of the volume rather than a wall or face, and where thecombinations have been modified from FIGS. A9-A10 to change thevolumetric density of the resulting unit cell. In FIG. A11, the heightof the node B130 has increased relative to the height of the volumeB132. Since the distal end of the strut B131 is fixed by the location ofa corner of the volume B132, the strut B131 must change its anglerelative to its attached node face so that it becomes nonorthogonal. Thenode B130 and strut B131 combination, where the angle of the strut B131from a horizontal plane is about 20.6 degrees, would be appropriate fora lattice structure with an elastic modulus of approximately 3 GPa.

In FIG. A12, the height of the node B230 relative to the height of thecube B232 has been increased over the ratio of FIG. A11 to create a nodeB230 and strut B231 combination that would be appropriate for a latticestructure with an elastic modulus of approximately 4 GPa. As the heightof the node B230 increases, the angle between the strut B231 and ahorizontal plane decreases to about 18.8 degrees. As the height of thenode B230 increases, the size of the node faces also increase so thatthe size of the strut B231 increases. While the distal end of the strutB231 is fixed to the corner of the volume B232, the size of the distalend increases to match the increased size of the node face to maintain asubstantially even strut diameter along its length. As the node andstrut increase in size, the volumetric density increases, as does theelastic modulus. In FIG. A13, the height of the node B330 relative tothe height of the volume B332 has been increased over the ratio of FIG.A13 to create a node B330 and strut B331 combination that would beappropriate for a lattice structure with an elastic modulus ofapproximately 10 GPa. In this configuration, the angle B333 between thestrut B331 and a horizontal plane decreases to about 12.4 degrees andthe volumetric density increases over the previous examples. The singlenode and strut examples can be copied and/or mirrored to create unitcells of appropriate sizes and characteristics. For instance, the anglebetween the strut and a horizontal plane could be increased to 25.8degrees to render a lattice with a 12.3 percent volumetric density andan elastic modulus of about 300 MPa. While a single node and singlestrut were shown in the examples for clarity, multiple struts may beattached to each node to create an appropriate unit cell.

Adjacent struts extending from adjacent node faces on either the upperhalf or lower half of the node have an angle from the horizontal planeand a lateral separation angle defined by an angle between the strutdirections of adjacent struts. In the MRDD and RDDR structures, adjacentstruts have an external edge or face of the elongate portion extendingclosest to the relevant adjacent strut. The lateral separation angle, asused herein, generally refers to the angle between an external edge orface of the elongate portion of a strut extending closest to therelevant adjacent strut. In some embodiments, a lateral separation angledefined by a line extending between the center of the strut end faces ora line defined by the center of mass of the struts can be used inreference to a similar calculation for an adjacent strut.

The lateral separation angle is the angle between the nearest face oredge of a strut to an adjacent strut. The lateral separation angle canbe measured as the smallest angle between the nearest edge of a strut tothe nearest edge of an adjacent strut, in a plane containing both strutedges. The lateral separation angle can also be measured as the anglebetween the nearest face of a strut to the nearest face of an adjacentstrut in a plane normal to the two strut faces. In embodiments withoutdefined strut edges or strut faces, the lateral separation angle can bemeasured as an angle between the nearest portion of one strut to thenearest portion of an adjacent strut. For a unit cell in a cubic volume,as the strut angle from the horizontal plane decreases, the lateralseparation angle approaches 90 degrees. For a unit cell in a cubicvolume, as the strut angle from the horizontal plane increases, thelateral separation angle approaches 180 degrees. In some embodiments, itis preferable to have a lateral separation angle greater than 109.5degrees. In some embodiments, it is preferable to have a lateralseparation angle of less than 109.5 degrees. In some embodiments, it ispreferable to have a lateral separation angle of between and includingabout 108 degrees to about 156 degrees. In some embodiments, it is morepreferable to have a lateral separation angle of between and including111 degrees to 156 degrees. In some embodiments, it is more preferableto have a lateral separation angle of between and including 108 degreesto 120 degrees. In some embodiments, it is most preferable to have alateral separation angle of between and including about 111 degrees to120 degrees. In some embodiments, it is more preferable to have alateral separation angle of between and including 128 degrees to 156degrees. In FIG. A14 is a side view, viewed from a corner of the cubeB432, of a single node B430 with two adjacent struts B431 & B434attached and where the lateral separation angle B443 is identified. Whenmeasured from the nearest edge of a strut to the nearest edge of anadjacent strut, the lateral separation angle B443 is about 116 degrees.

In some embodiments, a unit cell is built up from multiple sub-unitcells fixed together. In FIG. A15 is an isometric view of an exemplarysub-unit cell comprising a single node and four struts. In FIG. A16 isan isometric view of two sub-unit cells in a stacked formation where theupper sub-unit cell is inverted and fixed to the top of the lowersub-unit cell. In FIG. A17 is an isometric view of eight sub-unit cellsstacked together to form a single RDDR unit cell.

In FIG. A15, the node B530 is a square bipyramid, oriented so that thetwo peaks face the top and bottom of a cubic volume B532. In someembodiments, the volume B532 can be a cuboid volume, a hexahedronvolume, an amorphous volume or of a volume with one or morenon-orthogonal sides. The peaks refer to the point where four upperfaces meet and the point where four lower faces meet. The node B530 isoriented so that the horizontal vertices face the lateral sides of thecubic volume B532. The strut B531 is fixed to a lower face of the nodeB530 face on its proximate end and extends to the nearest corner of thecubic volume B532 at its distal end. The distal end of the strut B531can remain fixed to the cubic volume B532 even if the node B530 changesin size to adjust the sub-unit cell properties.

On the lower face of the node B530 opposite the face which strut B531 isfixed, the proximate end of strut B534 is fixed to the node B530. Thestrut B534 extends to the nearest corner of cubic volume B532 at itsdistal end. The strut B535 is fixed on its proximate end to an uppernode B530 face directed about 90 degrees laterally from the node B530face fixed to strut B531. The strut B535 extends to the nearest cornerof the cubic volume B532 at its distal end. On the upper face of thenode B530 opposite the face which strut B535 is fixed, the proximate endof strut B536 is fixed to the node B530. The strut B536 extends to thenearest corner of the cubic volume B532 at its distal end.

In some embodiments, the struts B531 & B534-B536 are octahedrons withtriangular faces. The strut face fixed to a node B530 face can besubstantially the same size and orientation of the node B530 face. Thestrut face fixed to the nearest corner of the cube B532 can besubstantially the same size as the strut face fixed to the node B530 andoriented on a substantially parallel plane. The remaining six faces canbe six substantially similar isosceles triangles with a first internalangle and a second internal angle larger than said first internal angle.The six substantially similar isosceles triangles can be fixed alongtheir long edges to an adjacent and inverted substantially similarisosceles triangle to form a generally cylindrical shape with triangularends.

When forming a sub-unit cell B540, it can be beneficial to add an eighthnode B538 to each corner of the cube B532 fixed to a strut B531 &B534-B536. When replicating the sub-unit cell B540, the eighth node B538attached to each strut end is combined with eighth nodes from adjacentsub-unit cells to form nodes located between the struts of adjacentsub-unit cells.

In FIG. A16 is a first sub-unit cell B540 fixed to a second sub-unitcell B640 to form a quarter unit cell B560 used in some embodiments. Thesecond sub-unit cell B640 comprises a square bipyramid node B630 is asquare bipyramid, oriented so that the two peaks face the top and bottomof a cubic volume. The node B630 is oriented so that the horizontalvertices face the lateral sides of the cubic volume. The strut B635 isfixed to a lower face of the node B630 face on its proximate end andextends to the nearest corner of the cubic volume at its distal end. Onthe lower face of the node B630 opposite the face which strut B635 isfixed, the proximate end of strut B636 is fixed to the node B630. Thestrut B636 extends to the nearest corner of cubic volume at its distalend. The strut B634 is fixed on its proximate end to an upper node B630face directed about 90 degrees laterally from the node B630 face fixedto strut B635. The strut B634 extends to the nearest corner of the cubicvolume at its distal end. On the upper face of the node B630 oppositethe face which strut B634 is fixed, the proximate end of strut B631 isfixed to the node B630. The strut B631 extends to the nearest corner ofthe cubic volume at its distal end.

The first sub-unit B540 is used as the datum point in the embodiment ofFIG. A16, however, it is appreciated that the second sub-unit cell B640or another point could also be used as the datum point. Once the firstsub-unit cell B540 is fixed in position, it is replicated so that thesecond sub-unit cell B640 is substantially similar to the first. Thesecond sub-unit cell B640 is rotated about its central axis prior tobeing fixed on the top of the first unit-cell B540. In FIG. A16, thesecond sub-unit cell B640 is inverted to achieve the proper rotation,however, other rotations about the central axis can achieve the sameresult. The first sub-unit cell B540 fixed to the second sub-unit cellB640 forms a quarter unit cell B560 that can be replicated and attachedlaterally to other quarter unit cells to form a full unit cell.

Alternatively, a full unit cell can be built up by fixing a first groupof four substantially similar sub-unit cells together laterally to forma square, rectangle or quadrilateral when viewed from above. A secondgroup of four substantially similar sub-unit cells rotated about theircentral axis can be fixed together laterally to also form a square,rectangle or quadrilateral when viewed from above. The second group ofsub-unit cells can be rotated about their central axis prior to beingfixed together laterally or inverted after being fixed together toachieve the same result. The second group is then fixed to the top ofthe first group to form a full unit cell.

In FIG. A17 is an example of a full unit cell B770 formed by replicatingthe sub-unit cell B540 of FIG. A15. The cube B532 defining the bounds ofthe sub-unit cell B540 is identified as well as the node B530 and strutsB531 & B534-B536 for clarity. The full unit cell B770 of FIG. A17 can beformed using the methods described above or using variations within theinventive concept.

Each strut extending from the node, for a given unit cell, can besubstantially the same length and angle from the horizontal plane,extending radially from the node. At the end of each strut, the strut ismirrored so that struts extending from adjacent node faces form arhombus shaped opening. Because the struts can be non-orthogonal to thenode faces, rhombuses of two shapes emerge. In this configuration, afirst group of four rhombuses extend radially from the node oriented invertical planes. The acute angles of the first group of rhombuses equaltwice the strut angle from the horizontal plane and the obtuse anglesequal 180 less the acute angles. Also in this configuration is a secondgroup of eight rhombuses extending radially so that a portion of thesecond group of eight rhombuses fall within the lateral separation anglebetween adjacent struts defining the first group of four rhombuses. Theacute angles of the second group of rhombuses can be about the same asthe lateral separation angle between adjacent struts that define thefirst group of four rhombuses and the obtuse angles equal 180 less theacute angles. The characteristics of a scaffold may also be described byits surface area per volume. For a 1.0 mm×1.0 mm×1.0 mm solid cube, itssurface area is 6.0 square mm. When a 1.0 cubic mm structure iscomprised of a lattice structure rather than a 100 percent volumetricdensity material, the surface area per volume can increasesignificantly. In low volumetric density scaffolds, the surface area pervolume increases as the volumetric density increases. In someembodiments, a scaffold with a volumetric density of 30.1 percent wouldhave a surface area of 27.4 square mm per cubic mm. In some embodiments,if the volumetric density was decreased to 27.0 percent, the latticewould have a surface area of 26.0 square mm per cubic mm and if thevolumetric density were decreased to 24.0 percent, the lattice wouldhave a surface area of 24.6 square mm per cubic mm.

The MRDD and RDDR structures disclosed herein also have the advantage ofan especially high modulus of elasticity for a given volumetric density.When used as a lattice or scaffold, an implant with an adequate modulusof elasticity and a low volumetric density can be achieved. A lowvolumetric density increases the volume of the implant available forbone ingrowth.

In Table 1, below, are a number of example lattice configurations ofvarious lattice design elastic moduli. An approximate actual elasticmodulus was given for each example, representing a calculated elasticmodulus for that lattice after going through the manufacturing process.The lattice structures and implants disclosed herein can be designed toa design elastic modulus in some embodiments and to an approximateactual elastic modulus in other embodiments. One advantage of thepresently disclosed lattice structures is that the approximate actualelastic modulus is much closer to the design elastic modulus than hasbeen previously achieved. During testing, one embodiment of a latticewas designed for a 4.0 GPa design elastic modulus. Under testing, thelattice had an actual elastic modulus of 3.1 GPa, achieving an actualelastic modulus within 77 percent of the design elastic modulus.

For each lattice design elastic modulus, a volumetric density, ratio ofdesign elastic modulus to volumetric density, surface area in mm², ratioof surface area to volumetric density and ratio of surface area tolattice design elastic modulus is given.

TABLE 1 Ratio of Lattice Approx. Design Ratio of Ratio of Design ActualElastic Surface Surface Area Elastic Elastic Volumetric Modulus toSurface Area to to Lattice Modulus Modulus Density Volumetric AreaVolumetric Design Elastic (GPa) (GPa) (percent) Density (mm²) DensityModulus 0.3 0.233 18.5 1.6 22.5 121.5 74.9 3 2.33 29.9 10.0 27.5 92.29.2 4 3.10 33.4 12.0 28.8 86.4 7.2 5 3.88 36.4 13.8 29.9 82.2 6.0 6 4.6538.8 15.5 30.7 79.1 5.1 7 5.43 40.8 17.2 31.3 76.9 4.5 8 6.20 42.1 19.031.8 75.4 4.0 9 6.98 43.2 20.8 32.1 74.3 4.0

Table of Example Lattice Structures Based on Lattice Design ElasticModulus in GPa

In some of the embodiments disclosed herein, the required strutthickness can be calculated from the desired modulus of elasticity.Using the following equation, the strut thickness required to achieve aparticular elastic modulus can be calculated for some MRDD and RDDRstructures:

Strut Thickness=(−0.0035*(Ê2))+(0.0696*E)+0.4603

In the above equation, “E” is the modulus of elasticity. The modulus ofelasticity can be selected to determine the required strut thicknessrequired to achieve that value or it can be calculated using apreselected strut thickness. The strut thickness is expressed in mm andrepresents the diameter of the strut. The strut thickness may becalculated using a preselected modulus of elasticity or selected todetermine the modulus of elasticity for a preselected strut thickness.

In some embodiments, the unit cell can be elongated in one or moredirections to provide a lattice with anisotropic properties. When a unitcell is elongated, it generally reduces the elastic modulus in adirection normal to the direction of the elongation. The elastic modulusin the direction of the elongation is increased. It is desirable toelongate cells in the direction normal to the direction of new bonegrowth contained within the interconnections, openings and central voids(if any). By elongating the cells in a direction normal to the desireddirection of reduced elastic modulus, the shear strength in thedirection of the elongation may be increased, providing a desirable setof qualities when designing a structural scaffold. Covarying the overallstiffness of the scaffold may augment or diminish this effect, allowingvariation in one or more directions.

In some embodiments, the sub-unit cells may be designing by controllingthe height of the node relative to the height of the volume that definesthe sub-unit cell. Controlling the height of the node can impact thefinal characteristics and appearance of the lattice structure. Ingeneral, increasing the height of the node increases the strutthickness, increases the volumetric density, increases the strength andincreases the elastic modulus of the resulting lattice. When increasingthe height of the node, the width of the node can be held constant insome embodiments or varied in other embodiments.

In some embodiments, the sub-unit cells may be designing by controllingthe volume of the node relative to the volume that defines the sub-unitcell. Controlling the volume of the node can impact the finalcharacteristics and appearance of the lattice structure. In general,increasing the volume of the node increases the strut thickness,increases the volumetric density, increases the strength and increasesthe elastic modulus of the resulting lattice. When increasing the volumeof the node, the width or height of the node could be held constant insome embodiments.

In Table 2, below, are a number of example lattice configurations ofvarious lattice design elastic moduli. An approximate actual elasticmodulus was given for each example, representing a calculated elasticmodulus for that lattice after going through the manufacturing process.The lattice structures and implants disclosed herein can be designed toa design elastic modulus in some embodiments and to an approximateactual elastic modulus in some embodiments. For each lattice designelastic modulus, a lattice approximate elastic modulus, a node height, avolumetric density, a node volume, a ratio of node height to volumetricdensity, a ratio of node height to lattice design elastic modulus and aratio of volumetric density to node volume is given.

TABLE 2 Ratio of Lattice Node Lattice Approx. Ratio of Height to Ratioof Design Actual Node Lattice Vol. Elastic Elastic Node Volumetric NodeHeight Design Density to Modulus Modulus Height Density Volume to Vol.Elastic Node (GPa) (GPa) (mm) (percent) (mm3) Density Modulus Volume0.30 0.23 0.481 18.5 0.0185 2.60 1.60 9.98 3.00 2.33 0.638 29.9 0.04322.14 0.21 6.91 4.00 3.10 0.683 33.4 0.0530 2.05 0.17 6.29 5.00 3.880.721 36.4 0.0624 1.98 0.14 5.82 6.00 4.65 0.752 38.8 0.0709 1.94 0.135.48 7.00 5.43 0.776 40.8 0.0779 1.90 0.11 5.23 8.00 6.20 0.793 42.10.0831 1.88 0.10 5.07 9.00 6.98 0.807 43.2 0.0877 1.87 0.09 4.93

Table of Example Lattice Structures Based on Lattice Design ElasticModulus in GPa

Some embodiments of the disclosed lattice structures are particularlyuseful when provided within an elastic modulus range between anincluding 0.375 GPa to 4 GPa. Some embodiments, more preferably, includea lattice structure with an elastic modulus between and including 2.5GPa to 4 GPa. Some embodiments include a lattice structure with avolumetric density between and including five percent to 40 percent.Some embodiments, more preferably, include a lattice structure with avolumetric density between and including 30 percent to 38 percent.

The lattice structures disclosed herein have particularly robust loadingand fatigue characteristics for low volumetric density ranges and lowelastic moduli ranges. Some embodiments of the lattice structures have ashear yield load and a compressive yield load between and including 300to 15000N in static and dynamic loading up to 5,000,000 cycles at 5 Hz.Some embodiments have a compressive shear strength and an axial loadbetween and including 300 to 15000N in static and dynamic loading up to5,000,000 cycles at 5 Hz. Some embodiments have a shear strength and anaxial load between and including 300 to 15000N in static and dynamicloading up to 5,000,000 cycles at 5 Hz. Some embodiments have atorsional yield load up to 15 Nm.

In one example, the inventive lattice structure has a volumetric densityof between and including 32 percent to 38 percent, an elastic modulusbetween and including 2.5 GPa to 4 GPa and a shear strength and an axialload between and including 300 to 15000N in static and dynamic loadingup to 5,000,000 cycles at 5 Hz. Some examples include a first set ofsubstantially homogeneous openings with a width of about 200 μm to 900μm and a second set of substantially homogenous openings with a width ofabout 1 to 15 times the width of the first set of openings, where thenumber of openings in the second set are provided at a ratio of about1:8 to 1:12 relative to the number of openings in the first set.

The disclosed structures can also have benefits when used inapplications where osteointegration is not sought or undesirable. Byincluding a growth inhibiting coating or skin on a structure, thelattice disclosed herein can be used to provide structural supportwithout providing a scaffold for bone growth. This may be desirable whenused in temporary implants or medical devices that are intended to beremoved after a period of time.

Also disclosed herein is a method of designing a porous structure foruse in medical implants. The method of design includes the steps of:

1. Modeling a sub-unit cell within a hexahedron volume of a preselectedheight, first width and second width, where the hexahedron volumecomprises six hexahedron volume faces.

2. Modeling a node centrally located within the hexahedron volume, wherethe node comprises a square bipyramid with eight node faces and a squareplane parallel to a face of said hexahedron volume, and the hexahedronvolume further comprises eight corners, each defined by the intersectionof three hexahedron volume faces.

3. Modeling a first strut fixed on its proximate end to a first nodeface and fixed on its distal end to a corner of the hexahedron volumenearest to the first node face.

4. Modeling a second strut fixed on its proximate end to a second nodeface, where the second node face is spaced about 180 degrees laterallyfrom the first node face.

5. Modeling a third strut fixed on its proximate end to a third nodeface, where the third node face is spaced about 90 degrees laterallyfrom the first node face.

6. Modeling a fourth strut fixed on its proximate end to a fourth nodeface, where the fourth node face is spaced about 180 degrees laterallyfrom the third node face.

The method of designing a porous structure for use in medical implantsmay optionally include the step of modeling a unit cell by replicatingthe sub-unit cell and creating a first grouping of four sub-unit cellsfixed to a second grouping of four sub-unit cells, where the firstgrouping comprises four substantially similar sub-unit cells arrangedand fixed laterally in a quadrilateral when viewed from above, and wherethe second grouping comprises four substantially similar sub-unit cellsinverted relative to the first grouping and fixed laterally in aquadrilateral when viewed from above.

When designing a porous structure for medical implants using the methoddisclosed herein, properties of the porous structure may be changed bychanging a property of the sub-unit cell. Changes to the sub-unit cellthat can change a property of the sub-unit cell include, but are notlimited to, changing the height of the node, changing the volume of thenode, changing a lateral dimension of the node, changing the height ofthe hexahedron volume, changing the first width of the hexahedronvolume, or changing the second width of the hexahedron volume. In someembodiments, it is preferable to select a predetermined height of thehexahedron volume that is less than the first width or second width ofthe hexahedron volume.

The disclosed method of design can include identifying a reference planedefined by a hexahedron volume face and selecting a strut directionbetween 0 degrees to 90 degrees from the reference plane. The disclosedmethod of design can also include identifying a reference plane definedby a hexahedron volume face and selecting a strut direction betweeneight degrees to 30 degrees from the reference plane.

The lattice structure used in the disclosed method of design can includevarious structures, including but not limited to a rhombic dodecahedron,a modified rhombic dodecahedron or a radial dodeca-rhombus.

The method of designing a porous structure for use in medical implantscan optionally further include the steps:

1. Identifying a principal axis defined by a line parallel to the heightof the hexahedron volume.

2. Identifying a loading axis within 90 degrees of the principal axis.

3. Identifying a second loading axis oriented at an angle offset fromthe loading axis.

4. Configuring the implant to provide an elastic modulus along theloading axis of between and including 0.3 GPa to 12 GPa and an elasticmodulus along the second loading axis of between and including 2 GPa to25 GPa, where the elastic modulus along the loading axis is less thanthe elastic modulus along the second loading axis.

The present invention disclosed herein also includes a biocompatiblelattice structure with anisotropic properties (hereinafter “anisotropiclattice”) and a method of use. Only the preferred embodiments are shownherein and it is understood that the use of other unit cell structureswould be within the inventive concept expressed herein.

In general, the elastic modulus of a lattice structure and thevolumetric density of that structure are related. Decreasing thevolumetric density decreases the elastic modulus and vice versa. When asubstantially isotropic lattice is used as a structural scaffold, theresulting implant may require a design compromise in at least onedirection. For example, a structural scaffold, if used in the spine,must be capable of resisting shear in the anterior-posterior directionand torsion around the superior-inferior axis while resistingcompression in the superior to inferior direction. If isotropic, astructural scaffold would have substantially identical properties in alldirections, requiring the structural scaffold to be designed based onthe highest forces expected in all directions. The anisotropic latticestructures of the present invention are preferably comprised of multipleunit cells that can be substantially the same or different for therelevant portion of the structure. The relevant portion of a structureis the portion of a structure where specific properties are required.The relevant portion may include many adjacent unit cells or a singleunit cell, depending on the specific properties required.

In the disclosure herein, the struts that define the unit cells andanisotropic lattice structures can be of substantially the same diameterfor a single unit cell or multiple unit cells. Varying the diameter ofthe struts can allow the mechanical properties of the resulting latticeto be changed without changing the overall shape of the unit cells.While the struts are sometimes described as substantially the samediameter, it is understood that manufacturing tolerances may not allowstruts of substantially the same diameter in certain applications. Inparticular, when the unit cell is smaller, the strut diameter is moredifficult to control. The concepts of the present invention could alsowork in an anisotropic lattice with struts of different diameters orvariations in the strut diameter.

The unit cells of the anisotropic lattice structures are describedherein as shortened or elongated in one or more directions. Because thesize of each unit cell can be scaled to suit a particular material ortargeted mechanical properties, a unit cell may be shortened orelongated then scaled to the appropriate size.

FIGS. 1-3 show a repeatable unit cell structure of a modified rhombicdodecahedron lattice 10 where the shape of the unit cells is defined bystruts 11. The example shown is of a single complete MRDD unit cell,which includes additional struts extending outward that show theinterfacing geometry of adjacent unit cells.

In FIG. 1 is an isometric view of the MRDD lattice 10. In FIG. 2 is afront view and in FIG. 3 is a bottom view of the MRDD lattice 10. Theside views and back view are substantially the same as the front view.The top view is substantially the same as the bottom view. In the MRDDlattice, each unit cell is a modified rhombic dodecahedron with twelvesides in the shape of rhombuses. Because the MRDD unit cell shown is anopen cell structure, each side of the MRDD is defined by four struts 11that form a rhombus in a flat plane.

The MRDD lattice 10 in this example is substantially isotropic, whereeach of the twelve sides of the unit cell are substantially the samesize and shape. The struts 11 that form the sides are also asubstantially equal length and thickness. As used herein, the term“substantially” includes values up to 10 percent above or below thereferenced value. In FIG. 2, the length of the section of MRDD lattice10 in the z direction is defined by height A. In the section of MRDDlattice 10 shown in FIG. 2, the height A is equal to the height of twounit cells. In FIG. 3, the length of the section of MRDD lattice 10 inthe x direction is defined by width B and the length of the section ofMRDD lattice 10 in the y direction is defined by width C. In the sectionof MRDD lattice shown in FIG. 3, width B and width C are equal to theheight of a single unit cell. Because the height A is equal to theheight of two unit cells, width B and width C are equal to one half ofheight A. Point AA is identified on FIGS. 2 & 3 for additional clarity.

The MRDD lattice 10 has largely isotropic properties when compressed inthe direction of the x, y and z axes. When the MRDD lattice 10 is usedin an interbody spinal fusion implant, the mechanical propertiesprovided by the lattice are substantially the same in the superior toinferior direction, the anterior to posterior direction and the lateraldirection. When used herein for direction or orientation, the superiorto inferior direction, the anterior to posterior direction and thelateral directions correspond to the z, x and y directions,respectively. These specific directional references are exemplary andused to the example orientations described herein.

When using a lattice as a structural support in an interbody spinalfusion implant, the lattice must have sufficient torsional and shearstrength on the transverse plane, a generally horizontal plane definedby the anterior to posterior and lateral directions. When an MRDD unitcell is designed to have sufficient torsional and shear strength on thetransverse plane, the elastic modulus in the superior to inferiordirection is often higher than optimal. A high elastic modulus in thesuperior to inferior direction can cause stress shielding of new bonegrowth, resulting in slow and weak new bone growth. Additionally, alattice of the same volumetric density may maintain thicker struts bythe mechanism of increasing the unit cell size and thus achieve greaterresistance to fatigue in all directions and a reduced stiffness in onedirection.

When the elastic modulus of an interbody spinal fusion implant in thesuperior to inferior direction is high, the interbody implant takes thephysiological load as the patient moves, rather than the new bonegrowth. In accordance with Wolff's law, new bone growth that is shieldedfrom stress is weaker than bone that is subject to normal mechanicalstimulation. Because an isotropic lattice has substantially identicalmechanical properties along the x, y and z axes, it is not as ideal foruse as a load bearing scaffold for bone growth as an anisotropiclattice.

FIGS. 4-6 show a repeatable unit cell structure of a first embodiment ofthe present invention. The first embodiment is an elongated MRDD lattice110 where the shape of the unit cells is defined by struts 111. Thefirst embodiment is a single complete elongated RDD cell with additionalstruts extending outward that represent portions of a repeatingstructure. In FIG. 4 is an isometric view, in FIG. 5 is a front view andin FIG. 6 is a bottom view of the elongated MRDD lattice 110. The sideviews and back view are substantially the same as the front view. Thetop view is substantially the same as the bottom view.

In the elongated MRDD lattice 110, each unit cell is the intersection ofelongated modified rhombic dodecahedrons defined by twelve sides in theshape of rhombuses. Because the elongated MRDD lattice 110 has an opencell structure, each side of the unit cell is defined by four struts 111that form a rhombus in a flat plane. The elongated MRDD lattice 110 iselongated in the x and y directions so that the width of a single cellis equal to width B and width C in the x and y directions, respectively,and the height of two cells is equal to half of height A. In otherwords, the width of a single cell in the x or y direction is twice theheight of a single cell in the z direction in this embodiment. Point BBis identified on FIGS. 5 & 6 for additional clarity.

To achieve an MRDD cell structure that is wider than tall, the length ofstruts in the cell are preferably changed, altering the dimension of thecell. This allows for preferential variation of a cell dimension in anydirection. In the example, struts are shortened in the verticaldirection, reducing the cell height and stiffness in that celldirection.

The elongated MRDD lattice 110 has anisotropic properties that make itparticularly useful as a scaffold for bone growth. By creating a unitcell that is wider than tall, the resulting scaffold has a lower elasticmodulus in the vertical direction than in the horizontal direction. Ifused in the spine, the resulting lattice would allow greater compressionin the superior to inferior direction, while maintaining a high shearstrength in the anterior to posterior and lateral directions. Thereduced elastic modulus in the superior to inferior direction reducesstress shielding and promotes fusion.

FIGS. 7-9 show a repeatable unit cell structure of a second embodimentof the present invention. The second embodiment is an elongated MRDDlattice 210 where the shape of the unit cells is defined by struts 211.The second embodiment is a stack of three complete elongated MRDD unitcells with additional struts extending outward that represent portionsof a repeating structure. In FIG. 7 is an isometric view, in FIG. 8 is afront view and in FIG. 9 is a bottom view of the elongated MRDD lattice210. The side views and back view are substantially the same as thefront view. The top view is substantially the same as the bottom view.

In the elongated MRDD lattice 210, each unit cell is the intersection ofelongated modified rhombic dodecahedrons defined by twelve sides in theshape of rhombuses. Because the elongated MRDD lattice 210 has an opencell structure, each side of the unit cell is defined by four struts 211that form a rhombus in a flat plane. The elongated MRDD lattice 210 iselongated in the x and y directions so that the width of a single cellin the x direction is equal to width B, the width of a single cell inthe y direction is equal to width C, and the height of two cells in thez direction is equal to half of height A. In other words, the width of asingle cell in the x and y directions is twice the height of a singlecell in the z direction in this embodiment. Point CC is identified onFIGS. 8 & 9 for additional clarity.

While the exemplary embodiments of the anisotropic lattice are elongatedby the same amount in the x and y directions relative to the zdirection, other ratios of width to height are within the inventivescope of the present invention. Depending on the specific applicationwhere the lattice structure is needed, the width in the x or y directioncan be any value other than the height in the z direction of a unitcell. While the description of the present invention defines theelongation of the unit cell relative to the x, y and z directions, thelattice structure can be rotated or oriented to create a lattice withthe proper mechanical properties for a specific application. Forinstance, the unit cells of the lattice could have a height in the zdirection that is greater than the width in the x and y directions forapplications where compression along the vertical axis is undesirable.The lattice structure may also be rotated to design a lattice forspecific mechanical properties in other than the horizontal and verticaldirections. It is also possible to obtain different mechanicalproperties in directions that are not 90 degrees apart.

The exemplary embodiments described herein use a width B that is equalto width C, however, it is appreciated that it could be desirable tocreate a unit cell with a width B that is not equal to width C. Bychanging the width of the unit cell in only one direction, differentmechanical properties may be achieved along that axis.

While the x, y and z axis have been used herein to describe the presentinvention, the anisotropic lattice described herein can be adapted tothe orientation or orientations needed for a particular purpose. Forinstance, the principal axis line does not need to be a straight orvertical line following the z axis. In one example, the principal axisline follows the lordosis of the spine. In another example, the latticestructure varies throughout to achieve an implant whose principle axisfollows the lordosis of the spine. The dimensions of each unit cell canbe identical for a relevant portion at one extreme or they can all bedifferent at the other extreme, depending on the mechanical propertiesdesired. The dimensions of unit cells can be organized in layers one ormore unit cell in height and one or more unit cell in width. Unit cellswithin a certain layer can share dimensional properties and thereforemechanical properties.

The shape of the unit cells can also be adjusted to increase thetorsional and shear strength of the lattice in the x and y directions.The torsional and shear strength can be adjusted by changing thedimensions of all unit cells or preferentially by only changing thedimensions of the cells in particular portions of the lattice structure.In one example, the unit cells are changed only near the top or bottomof the lattice structure.

The anisotropic lattice structures disclosed herein can be produced froma range of materials and processes. When used as a bone scaffold it isoften desirable for the anisotropic lattice to be made of abiocompatible material that allows for bone attachment, either to thematerial directly or through the application of a bioactive surfacetreatment. In one example, the anisotropic lattice is comprised of animplantable metal.

In another exemplary embodiment, the anisotropic lattice is comprised ofan implantable metal with an elastic modulus along the z axis in therange of bone. In one example, the elastic modulus in the z direction isfrom 0.3 to 2.0 GPa and the elastic modulus in the x and y directions isfrom 2.0 to 25.0 GPa. In another example, the elastic modulus in the zdirection is from 2.0 to 4.0 GPa and the elastic modulus in the x and ydirections is from 4.0 to 25.0 GPa. In another example, the elasticmodulus in the z direction is from 4.0 to 12.0 GPa and the elasticmodulus in the x and y directions is from 12.0 to 25.0 GPa. In anotherexample, the elastic modulus in the z direction is from 0.3 to 12.0 GPaand the elastic modulus in the x and y directions is from 10.0 to 25.0GPa. In another exemplary embodiment, the anisotropic lattice iscomprised of titanium or a titanium alloy with an elastic modulus alongthe z axis in the range of bone. In one example, the elastic modulus inthe z direction is from 0.3 to 2.0 GPa and the elastic modulus in the xand y directions is from 2.0 to 25.0 GPa. In another example, theelastic modulus in the z direction is from 2.0 to 4.0 GPa and theelastic modulus in the x and y directions is from 4.0 to 25.0 GPa. Inanother example, the elastic modulus in the z direction is from 4.0 to12.0 GPa and the elastic modulus in the x and y directions is from 12.0to 25.0 GPa. In another example, the elastic modulus in the z directionis from 0.3 to 12.0 GPa and the elastic modulus in the x and ydirections is from 10.0 to 25.0 GPa.

In some embodiments, the elastic modulus of a lattice can be referencedbased on a line bisecting an internal angle of a vertex of a rhombicopening. In one embodiment, the elastic modulus in a first direction ofloading, where the first direction is perpendicular to the linebisecting an internal angle of a vertex of a rhombic opening, is betweenand including 0.3 GPa and 12.0 GPa, the elastic modulus in a seconddirection of loading that is offset from the first direction is betweenand including 2.0 GPa to 25.0 GPa and where the elastic modulus in thefirst direction is less than the elastic modulus in the seconddirection.

The anisotropic lattice structures disclosed herein can also bedescribed as a porous structure for medical implants comprisingrepeating unit cells within a defined volume with a length along aprincipal axis, an x axis normal to the principal axis and a y axisnormal to the x axis, a loading direction within 90 degrees of theprincipal axis and where the elastic modulus of the structure is loweralong the loading direction than along the x axis. In some embodiments,the porous structure can have an elastic modulus that is lower along theloading direction than along the y axis. The lattice structure can alsobe provided, in some embodiments, as a plurality of layers of homogenousrepeating unit cells fixed along the x axis and y axis where at leastone layer has a higher modulus of elasticity along the loading directionthan an adjacent layer. In some embodiments with multiple layers ofrepeating unit cells, the loading direction of each layer can follow thelordosis of the spine. In some embodiments with multiple layers ofrepeating unit cells, the direction of each layer can follow thecurvature of the device. In some embodiments with multiple layers ofrepeating unit cells, the direction of each layer can follow thecurvature of the surrounding tissue or bone structures. As notedpreviously, some embodiments of the lattice structure can comprise arhombic dodecahedron structure, the modified rhombic dodecahedronstructure or a radial dodeca-rhombic structure.

Some embodiments of the anisotropic structures disclosed herein can havean elastic modulus in a loading direction between and including 0.3 GPato 12 GPa and an elastic modulus along the x axis between and including2 GPa to 25 GPa, where the elastic modulus in the loading direction isless than the elastic modulus along the x axis. In some embodiments, thelength along the principal axis is less than the length along the xaxis. In some embodiments, the length along the principal axis is lessthan the length along the y axis. In other embodiments, the length alongthe x axis is about the same as the length along the y axis.

In some embodiments optimized for promoting bone in-growth, theprincipal axis can be aligned with the desired direction of bone growth,where the desired direction of bone growth is the direction of bonegrowth away from a bony structure. Some embodiments optimized to promotebone in-growth can have a volumetric density between and including 5percent to 40 percent and more preferably a volumetric density ofbetween and including 30 percent to 38 percent. When optimized for bonein-growth, it is preferable for some embodiments of the lattice to havean elastic modulus in one direction of between and including 0.375 GPato 4 GPa. It can also be beneficial for the lattice structures to have acompressive shear strength and an axial load between and including 300to 15000N in static and dynamic loading up to 5,000,000 cycles at 5 Hzand a torsional yield load of up to 15 Nm.

The lattice structures disclosed herein, in some examples, can beincluded in medical implants when the lattice structure is configured topromote bone in-growth, where the lattice structure is configured forimplantation in an area between at least two bony structures where bonegrowth is desired, where bony structures are a portion of a patient'stissue near or abutting the bone fusion implant when implanted, where aprincipal axis intersects both of the two bony structures, where aloading axis is within 90 degrees of the principal axis, where thelattice structure is configured to provide the sole mechanical spacingbetween the two bony structures, where a second loading axis intersectsthe loading axis; and where the lattice structure has a lower modulus ofelasticity along the loading axis than along the second loading axis.

While bone attachment is desirable when the elongated lattice of thepresent invention is used as a bone growth scaffold, the presentinvention may be used for mechanical support within the body withoutbone ingrowth. In one example, the anisotropic lattice is comprised ofpolyether ether ketone (hereinafter “PEEK”), a commonly used polymer inmedical devices that does not allow for bone attachment without asurface treatment. It would be beneficial to use PEEK for temporaryimplants or for implants that may need to be removed in the future.Manufacturing processes that can be used to produce the presentinvention in PEEK include, but are not limited to, 3D printing andextrusion printing.

While an elongated MRDD has been shown herein as the unit cell structureof the preferred embodiments, there are many types of unit cellstructures that can be elongated in one or more directions. Possibleunit cell that are appropriate include, but are not limited to, rhombicdodecahedron, diamond, dodecahedron, square, pentagonal, hexagonal andoctagonal. An anisotropic lattice may be achieved with a unit cell usingas few as four sides. The changes in width relative to the height of aunit cell necessary to achieve the desired mechanical properties aredifferent for different unit cell shapes and materials.

The anisotropic lattice is preferably created using a repeatingelongated MRDD unit cell because of the unique strength to weight ratioof the structure. Due to the strength to weight characteristics of theelongated MRDD unit cell, the resulting anisotropic lattice can beproduced with a lower volumetric density for a given stiffness. Thelower volumetric density allows for a greater amount of volume for boneingrowth and can result in stronger new bone growth. In someembodiments, the anisotropic lattice is preferably created using arepeating elongated RDDR unit cell, also for its unique strength toweight characteristics.

The embodiments of the anisotropic lattice disclosed herein can be usedin a method of reducing stress shielding of new bone growth in spinalfusion procedures. In spinal fusion procedures, the damaged or diseasedspinal disc is removed and replaced with an interbody device thatprovides mechanical spacing between the endplates of the adjacentvertebrae and a path for new bone to grow between the adjacentvertebrae. Over time, new bone growth from the adjacent vertebraeeventually grow together and fuse into a single bone.

When an interbody device has excess rigidity or an unnecessarily highelastic modulus, it tends to take the strain when the patient moves,rather than the new bone growth. When this occurs, the new bone growthis shielded from stress and in accordance with Wolff's law, the new bonegrowth is weaker than that it would have been if subject to normalphysiological stresses. In the spine, controlling the elastic modulus inthe superior to inferior direction or in the direction defined by thelordosis of the spine is theorized to be important to the loading of newbone growth.

The present method of reducing stress shielding involves creating aninterbody device that provides some or all of the mechanical spacingbetween the endplates of the adjacent vertebrae with an anisotropiclattice comprised of one or more unit cells disclosed herein. Byrepeating one or more of the unit cells disclosed herein, the resultinginterbody device preferably has a lower elastic modulus in the superiorto inferior direction or the direction defined by the lordosis of thespine than in the anterior to posterior or lateral directions. A spinalfusion device using cells elongated in the anterior to posterior orlateral directions allows a reduced elastic modulus in the superior toinferior direction or the direction defined by the lordosis of the spinewithout significantly changing the torsional and shear strength in otherdirections.

A reduced elastic modulus in the superior to inferior direction or thedirection defined by the lordosis of the spine is desirable because itallows the endplates of the adjacent vertebrae to move in a limitedamount relative to one another, placing stress on the new bone growth.The strength of the interbody must remain high enough to provideadequate stability, but low enough to share loading, thereby preventingstress shielding in the new bone growth.

Also disclosed is a method of reducing stress shielding in all implants,steps comprising:

1. Providing an implant comprised at least in part of a latticestructure, where the lattice structure comprises repeating unit cellsconfigured to allow tissue in-growth.

2. Defining an implant space near or abutting two areas of tissue.

3. Defining a principal axis that intersects both of the two areas oftissue.

4. Defining a loading axis within 90 degrees of the principal axis.

5. Configuring the implant to provide the sole mechanical spacingbetween the two areas of tissue in at least one plane intersecting theloading axis; and

6. Configuring the repeating unit cells so that they are shorter alongthe loading axis than in any other direction.

In the above method, the repeating unit cells can use various latticestructures, including but not limited to a rhombic dodecahedron, amodified rhombic dodecahedron or a radial dodeca-rhombus. The implant ispreferably configured to be implanted near or abutting an area oftissue. The areas of tissue can be various types of tissue, includingbut not limited to, fibrous tissue or bony tissue. Areas of tissue canbe as small as a single cell and can be part of a continuous surface ortissue or bone. The plane intersecting the loading axis can be a flatplane, but is not necessarily so. The intersecting plane can be, forexample, a curved plane. The intersecting plane preferable defines acontinuous layer between the two areas of tissue where the latticestructure provides the sole mechanical spacing between the areas oftissue.

The above method of reducing stress shielding can include the steps of:

1. Identifying a second loading axis oriented at an angle offset fromthe loading axis.

2. Configuring the implant to provide an elastic modulus along theloading axis of between and including 0.3 GPa to 12 GPa and an elasticmodulus along the second loading axis of between and including 2 GPa to25 GPa, where the elastic modulus along the loading axis is less thanthe elastic modulus along the second loading axis.

In some aspects, what has been described is a biocompatible latticestructure, capable of design with anisotropic properties and a method ofreducing stress shielding of new bone growth in spinal fusionprocedures. While this disclosure describes the use of a lattice or ananisotropic lattice as a bone scaffold, all or part of the invention iscapable of being used in other applications. In this disclosure, thereare shown and described only the preferred embodiments of the invention,but, as aforementioned, it is to be understood that the invention iscapable of use in various other combinations and environments and iscapable of changes or modifications within the scope of the inventiveconcept as expressed herein.

1. A lattice structure for use in medical implants, comprising: alattice structure configured to promote tissue in-growth; wherein saidlattice structure provides sole initial mechanical spacing between atleast two areas of tissue; wherein said lattice structure comprisesrepeating unit cells; wherein said lattice structure defines a number ofopenings; wherein a first group of openings, openings A, have a width ofabout width A; wherein a second group of openings, openings B, have awidth of about width B; wherein width B is greater than width A; whereinsaid openings B are included at a ratio of about 1:1 to 1:25 per openingA in said lattice structure; and wherein said areas of tissue areportions of tissue near or abutting said implant when implanted.
 2. Thelattice structure of claim 1, wherein said unit cells further comprise arhombic dodecahedron structure defined by struts within an amorphousvolume.
 3. The lattice structure of claim 1, wherein said unit cellsfurther comprise a radial dodeca-rhombus structure defined by strutswithin an amorphous volume.
 4. The lattice structure of claim 1, whereinsaid lattice structure has a volumetric density between and including 5percent to 40 percent.
 5. The lattice structure of claim 1, wherein saidareas of tissue comprise bony structures.
 6. The lattice structure ofclaim 1, wherein said lattice structure has a volumetric density betweenand including 30 percent to 38 percent; and wherein said openings B areincluded at a ratio of about 1:8 to 1:12 per opening A in said latticestructure.
 7. The lattice structure of claim 1, wherein said latticestructure has an elastic modulus between and including 0.375 GPa to 4GPa.
 8. The lattice structure of claim 1, wherein said lattice structurehas a shear yield load and a compressive yield between and including 300to 15000N in static and dynamic loading up to 5,000,000 cycles at 5 Hz.9. The lattice structure of claim 1, wherein width A is between andincluding 200 μm to 900 μm, and wherein width B is 1 to 15 times aslarge as width A
 10. The lattice structure of claim 1, wherein saidlattice structure has a torsional yield load up to 15 Nm.
 11. Thelattice structure of claim 1, wherein said lattice structure has avolumetric density of 5 percent to 40 percent, an elastic modulusbetween and including 0.375 MPa to 4 GPa, a compressive shear strengthand an axial load between and including 300 to 15000N in static anddynamic loading up to 5,000,000 cycles at 5 Hz.
 12. The latticestructure of claim 1, wherein said lattice structure has a volumetricdensity of 32 percent to 38 percent, an elastic modulus between andincluding 2.5 GPa to 4 GPa and a shear strength and an axial loadbetween and including 300 to 15000N in static and dynamic loading up to5,000,000 cycles at 5 Hz.
 13. The lattice structure of claim 1, whereinsaid lattice structure has a volumetric density of 32 percent to 38percent, an elastic modulus between and including 2.5 GPa to 4 GPa, acompressive shear strength and an axial load between and including 300to 15000N in static and dynamic loading up to 5,000,000 cycles at 5 Hzand wherein said unit cells further comprise a rhombic dodecahedronstructure defined by struts within an amorphous volume.
 14. The latticestructure of claim 1, wherein said lattice structure has a volumetricdensity of 32 percent to 38 percent, an elastic modulus between andincluding 2.5 GPa to 4 GPa, a compressive shear strength and an axialload between and including 300 to 15000N in static and dynamic loadingup to 5,000,000 cycles at 5 Hz and wherein said unit cells furthercomprise a radial dodeca-rhombus structure defined by struts within anamorphous volume.
 15. A lattice structure for use in medical implants,comprising: a lattice structure comprising struts; wherein said latticestructure has an elastic modulus in a first direction of 0.375 GPa to 4GPa; wherein said lattice structure is configured to provide solemechanical spacing across a volume of desired bone growth, wherein saidvolume for desired bone growth is any area near or abutting at least twobony structures; wherein said struts define openings throughout thevolume of said lattice structure; wherein a first group of openings,openings A, comprise a plurality of said openings configured to promoteosteoblast in-growth; and wherein a second group of openings, openingsB, comprise a plurality of said openings configured to promote osteonin-growth.
 16. The lattice structure of claim 15, wherein said latticestructure further comprises repeating unit cells of a predeterminedamorphic volume containing a rhombic dodecahedron structure defined bystruts.
 17. The lattice structure of claim 15, wherein said latticestructure further comprises repeating unit cells of a predeterminedamorphic volume containing a radial dodeca-rhombus structure defined bystruts.
 18. The lattice structure of claim 15, wherein said latticestructure has a volumetric density between and including 5 percent to 40percent.
 19. The lattice structure of claim 15, wherein said two bonystructures are part of one continuous segment of bone.
 20. The latticestructure of claim 15, wherein said lattice structure has a volumetricdensity between and including 30 percent to 38 percent wherein saidopenings A have a substantially homogeneous width of about 200 μm to 900μm; and wherein said openings B have a substantially homogenous width ofabout 1 to 15 times said width of said openings A.
 21. The latticestructure of claim 15, wherein said lattice structure has a shear yieldload between and including 300 to 15000N in static and dynamic loadingup to 5,000,000 cycles at 5 Hz.
 22. The lattice structure of claim 15,wherein said lattice structure has a compressive yield load between andincluding 300 to 15000N in static and dynamic loading up to 5,000,000cycles at 5 Hz.
 23. The lattice structure of claim 15, wherein saidlattice structure has a torsional yield load up to 15 Nm.
 24. Thelattice structure of claim 15, wherein said lattice structure has avolumetric density of 32 percent to 38 percent, an elastic modulusbetween and including 2.5 GPa to 4 GPa and a shear strength and an axialload between and including 300 to 15000N in static and dynamic loadingup to 5,000,000 cycles at 5 Hz; wherein said openings A comprise asubstantially homogeneous width of about 200 μm to 900 μm; wherein saidopenings B comprise a substantially homogenous width of about 1 to 15times said width of said openings A; wherein a number of openings A areprovided in said lattice structure; and wherein a number of openings Bare provided in said lattice structure at a ratio of about 1:8 to 1:12relative to the number of openings A.